Consider the following.
[tex]g(x)=5 x+14[/tex]
(a) Find [tex]g(2)[/tex].
[tex]g(2)=24[/tex]
(b) Find [tex]g(-11)[/tex]
[tex]g(-11)=-41[/tex]
(c) Find [tex]x[/tex] such that [tex]g(x)=49[/tex].
[tex]x=[/tex]
Answer (1)
Set up the equation 5 x + 14 = 49 .
Subtract 14 from both sides to get 5 x = 35 .
Divide both sides by 5 to isolate x .
The solution is x = 7 .
Explanation
Problem Setup We are given the function g ( x ) = 5 x + 14 , and we want to find the value of x such that g ( x ) = 49 . In other words, we need to solve the equation 5 x + 14 = 49 for x .
Isolating the term with x To solve the equation 5 x + 14 = 49 , we first subtract 14 from both sides of the equation: 5 x + 14 − 14 = 49 − 14
Simplifying the equation This simplifies to: 5 x = 35
Solving for x Now, we divide both sides of the equation by 5 to isolate x :
5 5 x = 5 35
Final Answer This simplifies to: x = 7 Therefore, the value of x such that g ( x ) = 49 is 7.
Examples
Imagine you're running a small business where your profit, g(x), is determined by the number of items you sell, x. Your profit is calculated by the equation g(x) = 5x + 14, where 5 is the profit per item and 14 is the base profit. If you want to achieve a profit of 49, you need to determine how many items you must sell. By solving the equation 5x + 14 = 49, you find that you need to sell 7 items to reach your target profit of 49. This kind of problem helps in setting sales targets and understanding the relationship between sales volume and profit.
